%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN351+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:37:40 AM UTC 2026
% Result : Theorem 0.16s 0.44s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 3 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 13 ( 6 avg)
% Number of connectives : 72 ( 21 ~; 17 |; 20 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 2 sgn 20 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_18_3,conjecture,
! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,Y2,X1,Z)
=> ( ( big_f(X1,Y1,X1,Y2)
<=> big_f(Y1,X2,Y1,Y2) )
=> ( big_f(X1,Y1,X1,Y2)
=> ( ( big_f(X1,Z,Y1,Z)
=> ( big_f(X1,Y1,X1,Y2)
<=> big_f(X1,Y2,Y1,Y2) ) )
& ( big_f(X1,Y2,Y1,Y2)
=> big_f(X1,Z,Y1,Z) ) ) ) ) ),
file('theBenchmark.p',church_46_18_3) ).
fof(church_46_18_3_neg,negated_conjecture,
~ ! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,Y2,X1,Z)
=> ( ( big_f(X1,Y1,X1,Y2)
<=> big_f(Y1,X2,Y1,Y2) )
=> ( big_f(X1,Y1,X1,Y2)
=> ( ( big_f(X1,Z,Y1,Z)
=> ( big_f(X1,Y1,X1,Y2)
<=> big_f(X1,Y2,Y1,Y2) ) )
& ( big_f(X1,Y2,Y1,Y2)
=> big_f(X1,Z,Y1,Z) ) ) ) ) ),
inference(assume_negation,[status(cth)],[church_46_18_3]) ).
fof(nnf_1,plain,
? [X1,X2] :
! [Y1,Y2] :
? [Z] :
( ( ( ( ~ big_f(X1,Y2,Y1,Y2)
| ~ big_f(X1,Y1,X1,Y2) )
& ( big_f(X1,Y2,Y1,Y2)
| big_f(X1,Y1,X1,Y2) )
& big_f(X1,Z,Y1,Z) )
| ( ~ big_f(X1,Z,Y1,Z)
& big_f(X1,Y2,Y1,Y2) ) )
& big_f(X1,Y1,X1,Y2)
& ( ~ big_f(Y1,X2,Y1,Y2)
| big_f(X1,Y1,X1,Y2) )
& ( big_f(Y1,X2,Y1,Y2)
| ~ big_f(X1,Y1,X1,Y2) )
& big_f(X1,Y2,X1,Z) ),
inference(fof_nnf,[status(thm)],[church_46_18_3_neg]) ).
fof(sk_church_46_18_3_neg_sk,plain,
! [Y1,Y2] :
( ( ( ( ~ big_f(sK0,Y2,Y1,Y2)
| ~ big_f(sK0,Y1,sK0,Y2) )
& ( big_f(sK0,Y2,Y1,Y2)
| big_f(sK0,Y1,sK0,Y2) )
& big_f(sK0,sK1(Y1,Y2),Y1,sK1(Y1,Y2)) )
| ( ~ big_f(sK0,sK1(Y1,Y2),Y1,sK1(Y1,Y2))
& big_f(sK0,Y2,Y1,Y2) ) )
& big_f(sK0,Y1,sK0,Y2)
& ( ~ big_f(Y1,sK2,Y1,Y2)
| big_f(sK0,Y1,sK0,Y2) )
& ( big_f(Y1,sK2,Y1,Y2)
| ~ big_f(sK0,Y1,sK0,Y2) )
& big_f(sK0,Y2,sK0,sK1(Y1,Y2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X1,sK0),skolemize(X2,sK2),skolemize(Z,sK1(Y1,Y2))],[nnf_1]) ).
fof(sk_church_46_18_3_neg,plain,
( ! [VAR_0,VAR_1] :
( ~ big_f(sK0,VAR_1,VAR_0,VAR_1)
| ~ big_f(sK0,VAR_0,sK0,VAR_1)
| ~ big_f(sK0,sK1(VAR_0,VAR_1),VAR_0,sK1(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( big_f(sK0,sK1(VAR_1,VAR_0),VAR_1,sK1(VAR_1,VAR_0))
| big_f(sK0,VAR_0,VAR_1,VAR_0) )
& ! [VAR_0,VAR_1] : big_f(sK0,VAR_0,sK0,VAR_1)
& ! [VAR_0,VAR_1] :
( big_f(VAR_0,sK2,VAR_0,VAR_1)
| ~ big_f(sK0,VAR_0,sK0,VAR_1) )
& ! [VAR_0,VAR_1] : big_f(sK0,VAR_0,sK0,sK1(VAR_1,VAR_0)) ),
inference(cnf_transformation,[status(thm)],[sk_church_46_18_3_neg_sk]) ).
cnf(c_4,negated_conjecture,
big_f(sK0,A,sK0,B),
inference(split_conjunct,[status(thm)],[sk_church_46_18_3_neg]) ).
cnf(c_6,negated_conjecture,
( ~ big_f(sK0,B,A,B)
| ~ big_f(sK0,A,sK0,B)
| ~ big_f(sK0,sK1(A,B),A,sK1(A,B)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_18_3_neg]) ).
cnf(c_7,negated_conjecture,
( ~ big_f(sK0,B,A,B)
| ~ big_f(sK0,sK1(A,B),A,sK1(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_6]) ).
cnf(c_10,negated_conjecture,
~ big_f(sK0,A,sK0,A),
inference(resolve,[status(thm)],[c_7,c_4]) ).
cnf(c_9,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_4,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN351+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n004.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 17:37:21 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 2254918 was started by sandbox2 on n004,
% 0.16/0.43 % Sat Sep 26 17:37:21 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 0.16/0.44
% 0.16/0.44 % SZS status Theorem for theBenchmark
% 0.16/0.44
% 0.16/0.44 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.44 % Length of proof is 5.
% 0.16/0.44 % Level of proof is 3.
% 0.16/0.44 % Maximum clause weight is 14.000.
% 0.16/0.44 % Given clauses 3.
% 0.16/0.44
% 0.16/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------